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Exercise 10: Direct Shear Test CE 337, Section 13, Team 5 Experimental data acquired on April 28 th , 2009 by: Jane Doe (Role: A – Team Leader) John Doe (Role: B) Jonathan Doe (Role: B) Submittal Date: May 5 th , 2009 The Pennsylvania State University Department of Civil and Environmental Engineering

ABSTRACT The objective of the laboratory exercise presented in this report was to determine the shear strength – cohesion and internal friction angle – of a dry sand specimen in terms of total stress and to observe the specimen contraction and expansion during shearing. The test was performed using a standard direct shear apparatus consisting of a manual loading yoke for applying normal force to the specimen, a proving ring to measure the soil specimen’s resistance to shear, and manual dial gages for measuring the deflection of the proving ring, displacement of the shear box, and vertical expansion of the specimen. Displacement of the shear box was driven by the apparatus’ internal motor and occurred at a constant rate (i.e. the test was strain-controlled). Upon analysis of the experimental data, it was discovered that an error was made during testing. This error led to invalid results and as a consequence, the soil sample’s shear strength properties were unable to be determined. However, this testing error did not affect the volume change results, which indicated that the soil specimens were densely compacted.

TABLE OF CONTENTS Page ABSTRACT ........................................................................................................... ii TABLE OF CONTENTS ....................................................................................... iii LIST OF TABLES ................................................................................................. iv LIST OF FIGURES ................................................................................................. v INTRODUCTION ................................................................................................... 1 RESULTS AND DISCUSSION .............................................................................. 2 CONCLUSIONS ..................................................................................................... 7 REFERENCES ........................................................................................................ 8 APPENDIX A: RAW DATA ................................................................................... 9

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LIST OF TABLES Page Table 1 Determination of Normal Stress on Soil Specimens During Testing ..................... 2 Table 2 Direct Shear Experimental Data for Specimen 1 – Normal Load = 2.5 psi ........... 2 Table 3 Direct Shear Experimental Data for Specimen 2 – Normal Load = 5 psi .............. 3 Table 4 Direct Shear Experimental Data for Specimen 3 – Normal Load = 10 psi ............ 4 Table 5 Typical Values of Drained Angle of Friction for Sand and Silts (after Das 2006) ............................................................................................................................. 5

LIST OF FIGURES Page Figure 1 Shear stress vs. displacement for each specimen ................................................. 5 Figure 2 Mohr-Coulomb failure envelope for tested soil ................................................... 6 Figure 3 Contraction and expansion of each specimen during shearing ............................. 6

INTRODUCTION The shear strength properties of soil, typically defined in terms of the soil’s cohesion (c) and internal angle of friction ( ), represent the soil’s per-unit-area ability to resist sliding along a ϕ plane within the soil mass. Quantification of these strength properties and a thorough understanding of their nature are essential in the design of stable earth structures such as foundations, slopes, and earth-retaining structures. The test is performed according to ASTM D 3080-04. The test method consists of placing a soil specimen in the direct shear device (Figure 1), applying a pre-determined normal stress, and shearing the specimen at a constant strain rate. At a given normal stress, the shear strength, which is the maximum shear resistance can be obtained. The shear strengths (τ) are plotted against the normal stress (σ) to obtain the Mohr- Coulomb failure envelope, which is assumed to be linear (Figure 2). Figure 1: Picture (left) and schematics of direct shear test setup Figure 2: Typical results obtained from direct shear test

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RESULTS AND DISCUSSION Table 1 presents the measurements and calculated values used to determine the normal stress on each of the three specimens. Table 1 Determination of Normal Stress on Soil Specimens During Testing Property Specimen 1 2 3 Cross-sectional area, A (in 2 ) 4.3 4.3 4.3 Normal load (lb) 44 88 132 Normal stress (psi) 10 20 30 Table 2 through Table 4 present the experimental data acquired during the direct shear testing of the three specimens as well as the calculated shear stress. Table 2 Direct Shear Experimental Data for Specimen 1 – Normal Load = 2.5 psi Horizontal Displacement (in) Vertical Displacement (in) Proving Ring Dial Gauge Reading, L (in) Shear Force, T = 199.71L + 2.5562 (lb) (L in mm) Shear Stress, τ = T/A (psi) 0.0000 0.0000 0.0000 2.6 0.6 0.0198 -0.0009 0.0004 4.5 1.1 0.0396 -0.0016 0.0004 4.5 1.1 0.0594 -0.0022 0.0005 5.0 1.2 0.0792 -0.0027 0.0008 6.8 1.6 0.0991 -0.0040 0.0023 14.1 3.3 0.1189 -0.0082 0.0034 20.1 4.7 0.1387 -0.0111 0.0047 26.5 6.2 0.1585 -0.0126 0.0059 32.7 7.6 0.1783 -0.0133 0.0073 40.0 9.3 0.1981 -0.0128 0.0085 46.3 10.8 0.2179 -0.0111 0.0096 51.5 12.0 0.2377 -0.0092 0.0101 54.5 12.7 0.2576 -0.0083 0.0107 57.3 13.4 0.2774 -0.0079 0.0109 58.6 13.7 0.2972 -0.0075 0.0112 59.7 13.9 0.3170 -0.0066 0.0105 56.3 13.1 0.3368 -0.0051 0.0102 54.8 12.8 0.3566 -0.0031 0.0100 53.8 12.6 0.3764 -0.0017 0.0099 53.1 12.4 0.3962 -0.0012 0.0094 50.5 11.8

Table 3 Direct Shear Experimental Data for Specimen 2 – Normal Load = 5 psi Horizontal Displacement (in) Vertical Displacement (in) Proving Ring Dial Gauge Reading, L (in) Shear Force T = 199.71L + 2.5562 (lb) (L in mm) Shear Stress τ = T/A (psi) 0.0000 0.0000 0.0000 2.6 0.6 0.0198 0.0000 0.0005 5.0 1.2 0.0396 0.0000 0.0005 5.0 1.2 0.0594 0.0000 0.0008 6.6 1.5 0.0792 -0.0002 0.0012 8.5 2.0 0.0991 -0.0005 0.0037 21.3 5.0 0.1189 -0.0037 0.0069 38.1 8.9 0.1387 -0.0063 0.0102 54.9 12.8 0.1585 -0.0071 0.0127 67.7 15.8 0.1783 -0.0072 0.0144 76.4 17.8 0.1981 -0.0066 0.0161 85.2 19.9 0.2179 -0.0049 0.0172 90.4 21.1 0.2377 -0.0034 0.0186 98.0 22.9 0.2576 -0.0018 0.0194 102.0 23.8 0.2774 0.0004 0.0197 103.6 24.2 0.2972 0.0024 0.0200 104.8 24.4 0.3170 0.0046 0.0195 102.4 23.9 0.3368 0.0061 0.0187 98.4 23.0 0.3566 0.0066 0.0179 94.0 21.9 0.3764 0.0067 0.0169 89.2 20.8

Table 4 Direct Shear Experimental Data for Specimen 3 – Normal Load = 10 psi Horizontal Displacement (in) Vertical Displacement (in) Proving Ring Dial Gauge Reading, L (in) Shear Force, T = 199.71L + 2.5562 (lb) (L in mm) Shear Stress, τ = T/A (psi) 0.0000 0.0000 0.0000 2.6 0.6 0.0198 -0.0009 0.0039 22.7 5.3 0.0396 -0.0015 0.0039 22.7 5.3 0.0594 -0.0017 0.0039 22.7 5.3 0.0792 -0.0021 0.0044 24.9 5.8 0.0991 -0.0024 0.0050 28.1 6.6 0.1189 -0.0037 0.0125 66.5 15.5 0.1387 -0.0046 0.0176 92.8 21.7 0.1585 -0.0053 0.0226 118.4 27.6 0.1783 -0.0052 0.0262 136.8 31.9 0.1981 -0.0049 0.0296 154.3 36.0 0.2179 -0.0042 0.0322 167.5 39.1 0.2377 -0.0034 0.0338 175.5 40.9 0.2576 -0.0017 0.0344 178.7 41.7 0.2774 -0.0005 0.0340 176.7 41.2 0.2972 0.0003 0.0330 171.5 40.0 0.3170 0.0009 0.0304 158.3 36.9 0.3368 0.0012 0.0282 146.7 34.2 0.3566 0.0012 0.0275 143.2 33.4 0.3764 0.0015 0.0262 136.8 31.9 From this experimental data, Figure 3 was created to show the relationship between the shear stress (the specimen’s resistance to shearing) and displacement during shearing for each specimen. The peak value represents the specimen’s shear strength and can be taken from the plots or directly from the experimental data. When plotted against the corresponding normal stress, three failure points are generated as in Figure 4. A best-fit line is applied to these points (shown in Figure 4) and compared with Equation 1 to determine the soil’s cohesion and internal angle of friction. The resulting value of internal angle of friction (54  ) far exceeds the expected values for any of the materials outlined in Table 5 from Das (2006).

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Table 5 Typical Values of Drained Angle of Friction for Sand and Silts (after Das 2006) Soil Type φ (deg) Sand: Rounded grains Loose 27-30 Medium 30-35 Dense 35-38 Sand: Angular grains Loose 30-35 Medium 35-40 Dense 40-45 Gravel with some sand 34-48 Silts 26-35 Upon further investigation after making this observation, the authors discovered that the data acquired from the proving ring were erroneous. When the machine is in operation, the proving ring can be subjected to either compressive or tensile forces, depending on the direction of displacement of the shear box. Correct usage of the equipment requires that the proving ring be compressed. However, in the experiment presented here, data was acquired while the proving ring was in tension. This error essentially invalidates all results aside from the contraction/dilation data, which does not rely on the direction of shear. Figure 3 Shear stress vs. displacement for each specimen. 0 10 20 30 40 50 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Shearstress(psi) Horizontaldisplacement(in) Normal stress = 10 psi Normal stress = 20 psi Normal stress = 30 psi 41.7 24.4 13.9

10, 13.9 20, 24.4 30, 41.7 y = 1.39x - 1.1333 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 Shearstress,τ(psi) Normalstress,σ(psi) Figure 4 Mohr-Coulomb failure envelope for tested soil. Despite the experimental error just described, the variation in specimen volume caused by particle rearrangement during shearing is still valid. Figure 5 presents this behavior for each specimen, and was generated from the data in Table 2 through Table 4. The initial contraction followed by expansion exhibited by each specimen indicates each was densely compacted. -0.015 -0.010 -0.005 0.000 0.005 0.010 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Ver caldisplacement(in) Horizontaldisplacement(in) Normal stress = 10 psi Normal stress = 20 psi Normal stress = 30 psi Figure 5 Contraction and expansion of each specimen during shearing.

CONCLUSIONS The main objectives of this exercise were to determine the shear strength properties – cohesion and internal angle of friction – for a soil sample. A secondary objective was to observe volume change behavior during shearing. Each objective was pursued via standard direct shear testing. Upon analysis of the experimental data, it was discovered that an error was made during testing. This error led to invalid results and as a consequence, the soil sample’s shear strength properties were unable to be determined. However, this testing error did not affect the volume change results, which indicated that the soil specimens were densely compacted. In the future, the authors suggest that tests performed using the correct mode of shearing (i.e. with the proving ring in compression).

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REFERENCES Das, B. M. (2006). “Shear Strength of Soil.” Principles of Geotechnical Engineering, Sixth Edition , Thomson Learning, Toronto, Ontario, Canada

APPENDIX A: RAW DATA Raw data was collected electronically during testing (i.e. no hand-written data sheets exist) and was presented in Table 1 through Table 4.